“When
you and I were in school, we used to just memorize 9 plus 6 equals 15. Not
anymore. With the Common Core, students need to understand why that’s the
case.”

This is
the introduction to the first of six “Homework Helper” segments Buffalo,
N.Y., NBC affiliate WGRZ is broadcasting this week in honor of
back-to-school week. The series is meant to be a helpful tool for parents
confused by their children’s Common Core homework this year.

Each
morning, a local math teacher takes one simple homework question, and spends a
few minutes explaining the methodology required to solve it. Each lesson takes
a little over one minute for the teacher to explain.

But
here’s the irony: the one-minute lessons are explaining long processes for
simple problems like 9 plus 6 — math that took children a few seconds to solve
before Common Core standards.

The article contains the
YouTube videos that are being shown to Buffalo parents.

A long time ago I studied mathematics at uni, got an honours degree, but went no further as I realized I had at best a second class mathematical brain. Studied law instead, where of course brains don't matter. Har. But I digress.

In elementary algebra we had 6 education students come into the class every morning. They planned to be math teachers.

I can't answer for their other mental skills and talents, but at mathematics they were third or fourth class brains. It was pitiful, awful, embarrassing. Their questions and answers showed that they knew little and could not do elementary logical reasoning. The rest of us felt very badly, tutored them, mentored them, nothing worked. They dropped out at half term.

What JKB said. You didn't just memorize, you were taught number theory using the pedagogical device of the number line. You knew that 9+6=15 because you start at 9 on the number line and add (i.e., move to the right) 6 places.

The Common Core approach is not dissimilar to the second example that JKB gave, but it skips the intermediate step and instead "borrows" the 1 from the 6, rather like we were taught to do in subtraction. So the Common Core approach does:9+1=1010+5=15.

It's not a crazy thing to teach kids how to do addition or subtraction by converting one of the numerals to the base. It seems unduly complex when working in base 10 because we are intuitively comfortable in base 10. But the skill is useful when working in number systems with number systems having different bases, i.e., base 16. This is similar to the same mental process I would have to go through to add, say, 9+9 in base 16.

This is how I add even today. Of course it's so fast now it's automatic, and it's pretty close to simply consulting a memorized fact in my head, but if I concentrate while I'm adding, I'm always sort of confirming that 9 plus 6 is 1 out of the 6 to make 10, and 5 more to make 15.

Same sort of thing works when multiplying, too. But see feynman on memorization. On the other hand, a young physicist, on saying he could always look up the physical constants when he needed them, was reproved: Feynman always had those things at his fingertips.

I keep the things at my fingertips that I use all the time, which certainly includes the memorized tables of addition and multiplication. When I was doing analytical geometry problems all the time, I memorized lots of trig relationships, too, so I'd have a toolbox for substituting things in and figuring how to crack a problem. I don't do those problems any more, so I'd look them up if I needed them.

Honestly, I don't mind the idea of pointing the 9 + 1 + 5 kind of thing out to kids the first time. After that, though, they should just drill until it's second nature.

I watched the video and wondered why the teacher started with breaking 6 into 5 + 1. She could also have broken 6 into 4 + 2 or 3 + 3. So the teacher's first step assumes the last step. So to make 10 work, you have to start with subtracting 9 from 10, then use the 1 and subtract it from 6.

The result: this is not a process which makes sense, and going through these subordinate calculations is hardly easier and faster than just memorizing. When the students get beyond adding and subtracting, not to mention multiplication and division, they will want something quicker and easier than chains of manipulations; they will want memorized calculations.

Also, per my comment above, the student has to memorize that 6 - 1 = 5. So the entire project which pretends to avoid memorization actually involves memorization. Suppose we just get honest about memorization and get on with it.

Strange. I think I always approach a simple addition of single digits by automatically "filling up" until I make an even ten (that's 1 to move over into the tens' place) and then figuring out how much I have left over for the ones' place. But obviously I don't stop to think about it unless I'm having one of those moments when ordinary facts seem unfamiliar, and I need a reality check. You know, like when the correct spelling of an ordinary word suddenly looks odd.